In the first specific decoding stage, we learn to detect the edges of each instance object.
In order to handle the imbalance between the two binary classes (edge, no edge), we used the HED-loss function [1]} a class-balanced cross-entropy function.
Then we consider the edge-class objective function as
\( \begin{aligned}\mathcal {L}_{\mathit {c}} =& -\beta \sum _{i \in Y_+} \log P \left( y_i=1 \:\vert \:X; \theta \right) \\& - (1-\beta ) \sum _{j \in Y_-} \log P \left( y_j=0 \:\vert \:X; \theta \right),\end{aligned}\) 
